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arXiv · 2103.12932

Based modules over the $\imath$quantum group of type AI

Hideya Watanabe
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Abstract

This paper studies classical weight modules over the $\imath$quantum group $\mathbf{U}^{\imath}$ of type AI. We introduce the notion of based $\mathbf{U}^{\imath}$-modules by generalizing the notion of based modules over the quantum groups. We prove that each finite-dimensional irreducible classical weight $\mathbf{U}^{\imath}$-module with integer highest weight is a based $\mathbf{U}^{\imath}$-module. As a byproduct, a new combinatorial formula for the branching rule from $\mathfrak{sl}_n$ to $\mathfrak{so}_n$ is obtained.

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Hideya Watanabe. 2021-03-24. Based modules over the $\imath$quantum group of type AI. https://arxiv.org/abs/2103.12932

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